Scattering below the ground state for the 2D non-linear Schrödinger and Klein-Gordon equations revisited

Abstract: We revisit the scattering problems for the 2D mass super-critical Schr\"{o}dinger and Klein-Gordon equations with radial data below the ground state in the energy space. We give an alternative proof of energy scattering for both defocusing and focusing cases using the ideas of Dodson-Murphy \citep{dodson2017new-radial}. Our results also include the exponential type nonlinearities which seems to be new for the focusing exponential NLS.